Biostats test 2 Flashcards
deviation score
xi-x bar
sample variance
sum of all squared deviation scores divided by n-1. (s squared)
purpose of ANOVA
splitting total variance in two parts; one pertaining to differences between groups and one pertaining to differences within groups.
F
mean squares between groups (explained varianace; effect)/mean squares within groups (unexplained variance; error). if F takes on a sufficiently large value, we can reject H0 (still need to compare p versus alpha.
another definition of variance
total sum of squares divided by n-1
total sum of squares
basically the top half of variance; sum of squared deviation scores between all n data points (summed over all groups), relative to the grand mean (mean of all those n data points). between groups sum of squares + within groups sum of squares
within groups sum of squares
sum of squared deviation scores between each of k group’s individual values relative to that k group’s mean, summed over all groups
between groups sum of squares
sum of squared deviation scores between each between of k group means relative to grand mean
degrees of freedom
number of values that are free to vary given a boundary condition
how many degrees of freedom does variance have
n-1 because given a mean value, one degree of freedom is lost to compute the variance around the mean
df total sum of squares
n-1 because one mean is constrained by the others
df between groups sum of squares
k-1, one mean is constrained by the others
df within groups sum of squares
n-k (one degree of freedom is used up in calculating each groups mean, so since there are k groups ,we lost k degrees of freedom, one for each group mean)
mean squares
computed on basis of different sums of squares by dividing the sums of squares by their degrees of freedom; so mean squares for total squares is actually variance!
one way ANOVA
one factor, eg drug dose on mean reaction time
Assumptions for one way anova
within group variability is unexplained; considered error variance. we check for unequal precision using Levene’s
Levene’s test for homogeneity of error variance
H0: all of the group’s distribution and errors differ in approximately the same way, regardless of the mean for each group.
Factorial anova
two factors or more, can each have different levels. for example three drug dose levels and two biological sexes. 3x2 = 6 mean values. then we can also have interactions.
effect modification
effect of one IV on DV is different for levels of another IV
mushrooming
when adding factors to design multiplies effect modification terms
independent samples t-test
two independent groups, compare their means; like one way anova with just two levels
repeated measures t dest
matched, dependent samples t-test: comparison of paired values
one-sample t-test
on sample mean compared to a given, fixed value
